23.1.404 problem 391

Internal problem ID [5011]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 391
Date solved : Tuesday, September 30, 2025 at 11:22:53 AM
CAS classification : [_Chini]

\begin{align*} x^{k} y^{\prime }&=a \,x^{m}+b y^{n} \end{align*}

✗ Maple

ode:=x^k*diff(y(x),x) = a*x^m+b*y(x)^n; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=x^k*D[y[x],x]==a*x^m + b*y[x]^n; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
k = symbols("k") 
m = symbols("m") 
n = symbols("n") 
y = Function("y") 
ode = Eq(-a*x**m - b*y(x)**n + x**k*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (a*x**m + b*y(x)**n)/x**k cannot be solved by the factorable group method